Understanding the relationship between

We describe the spatio-temporal dynamics of malaria transmission intensity measured by mosquito density and EIR in the KEMRI/CDC health and demographic surveillance system using entomological data collected during 2002–2004. Geostatistical zero inflated binomial and negative binomial models were applied to obtain location specific (house) estimates of sporozoite rates and mosquito densities respectively. Model-based predictions were multiplied to estimate the spatial pattern of annual entomological inoculation rate, a measure of the number of infective bites a person receive per unit of time. The models included environmental and climatic predictors extracted from satellite data, harmonic seasonal trends and parameters describing space-time correlation.

Spatio-temporal maps of malaria transmission intensity obtained in this study are not only useful in understanding variability in malaria epidemiology over small areas but also provide a high resolution exposure surface that can be used to analyse the impact of transmission on malaria related and all-cause morbidity and mortality.

Malaria parasites are transmitted from human to human via the bite of an infected female anopheline mosquito. The life cycle of the mosquito vector and the malaria parasite are strongly influenced by climatic factors, primarily rainfall, temperature and humidity. Suitable rainfall provides mosquito breeding sites and temperature influences both vector and parasite development. By understanding the relations between environmental/climatic factors and malaria transmission in space and time, transmission intensity can be estimated in areas where data are otherwise lacking and high risk areas can be identified. Understanding spatial and temporal variation in vector density and transmission intensity is useful in planning effective malaria control programs and determining the optimal allocation of limited resources.

Malaria transmission intensity is often assessed by the entomological inoculation rate (EIR) which is the product of the vector biting rate and the sporozoite rate (SR) which is the proportion of mosquitoes with sporozoites in their salivary glands [

Mosquito population size and sporozoite rates fluctuate between seasons and over years [

In the KEMRI/CDC Health and demographic surveillance systems (HDSS), entomological data are collected from randomly selected locations (houses) as part of routine surveillance to assess the effects of interventions aimed at reducing malaria transmission intensity. The main characteristics of the data are the presence of spatio-temporal correlation and the large number of locations without mosquitoes (zeros). Spatial correlation arises because neighbouring locations are influenced by similar exposures such as climate and environment due to close proximity of locations. Analyzing these data without taking into account these specific characteristics result in overestimation or underestimation of the statistical significance of the covariates [

Several studies have reported large spatio-temporal variations in mosquito density, SR and EIR [

In our previous work [

This study was carried out in the KEMRI/CDC HDSS site located in Asembo (Rarieda Division, Bondo District), Gem (Yala and Wagai Divisions, Siaya District) and Karemo (Karemo Division, Siaya District) areas situated in Nyanza Province, rural Western Kenya (Figure

Location of the KEMRI/CDC HDSS site.

During the study period, the KEMRI/CDC HDSS was only operating in Asembo, bordering Lake Victoria and Gem, adjacent to and North of Asembo. The HDSS has been described elsewhere in detail [^{2} with a population of 135,000 living in 33,990 households within 21,477 compounds.

Malaria is holoendemic in the KEMRI/CDC HDSS area where it is transmitted by

The entomological data (2002–2004) used in this study has been described elsewhere in detail [

The entomological inoculation rate (EIR) was calculated as the product of light trap densities and the proportion of infected mosquitoes (sporozoite rate). Mosquito density in the light traps was calculated by dividing the number of mosquitoes caught by the CDC light traps by the number of trap-nights. This estimate was then adjusted by multiplying by 1.605 as described by Lines and colleagues to calibrate the light trap estimates to those of human landing catch [

The climatic and environmental predictors used in this study are similar to the ones used by Amek et al. [

Land surface temperature for day and night (LST) and Normalized Difference Vegetation Index (NDVI) were extracted at 0.25 km by 0.25 km and 1 km by 1 km spatial resolution respectively from Moderate Resolution Imaging Spectroradiometer (MODIS). NDVI is a proxy measure of vegetation cover ranging from 1 to −1. Positive values indicate the presence of vegetation and negative values and values close to zero represent barren soil or water surfaces.

Elevation (distance above the sea level) data were extracted at 1 km resolution from a Digital Elevation Model (DEM). MODIS and DEM were obtained from U.S Geological Survey (USGS) EROS Data Center. Rainfall estimate (RFE) data with an 8 km by 8 km spatial resolution from Meteosat 7 satellite were also obtained from the Africa Data Dissemination Service (ADDS).

All environmental factors were extracted for each location and lags up to 3 months were created to account for possible elapsing (lag) time, between the predictive variables (rainfall, LST and NDVI) and the outcome variable (mosquito density).

The lag time analysis was carried out in STATA (version 9.0) to determine the best combination of lags that estimated the mosquito population density taking into account seasonality, distance to water bodies and elevation. Seasonality was modeled by (i) trigonometric functions with a cycle of 12 months [

The Akaike’s information criterion [

The assessment of model predictive ability was also similar to that carried out by [

The Bayesian model was fitted in OpenBUGS version 3.1.2 (Imperial College and Medical Research Council, London, UK) and Kriging was carried out in a code written by the authors in Fortan 95 (Digital Equipment Corporation) using standard numerical libraries (Numerical Algorithms Group Ltd). A description of the Bayesian geostatistical formulation model fitted to mosquito count data is given in the appendix.

A total of 2309 anopheline mosquitoes were collected from 3850 catches in 1110 unique locations during the study period. About 68 % of these locations had no mosquitoes.

Monthly pattern of average number of Anopheles gambiae and funestus species in relation to total Rainfall.

Figure

Monthly pattern of observed, fitted and predicted density of Anopheles gambiae mosquito.

Model validation showed that 83 % and 66 % of the test locations had mosquito densities which were within the 95 % credible intervals estimated from the zero inflated spatio-temporal negative binomial model and zero inflated spatial negative binomial model respectively. Furthermore, the zero inflated spatio-temporal negative binomial model consistently included the highest proportion of test locations in all the credible intervals compared to spatial negative binomial model (Figure

Proportion of test locations with none-zero mosquitoes falling in between 5 % to 95 % credible intervals of the posterior predictive distribution.

The best fitting zero-inflated spatiotemporal model included the following parameters: distance to water bodies, elevation, average value of NDVI and LSTN during the month of mosquito collection, average LSTD during the current and the previous month of mosquito collection, total rainfall during the current and the two previous months of mosquito collection, year trend, trigonometric seasonality, spatial and temporal variations. The results of bivariate non-spatial and spatio-temporal zero-inflated negative binomial models are shown in Table

Posterior estimates of zero inflated geostatistical density models

Covariates | Bivariate non-spatial | Spatiotemporal model |
---|---|---|

Mean (95 % CI) | Median (95 % CI) | |

Intercept | - | 4.634 (0.005,7.098) |

Distance to water body | −0.003 (−0.006,0.001) | −0.007 (−0.013,-0.002) |

Elevation | 0.002 (−0.001,0.003) | −0.008 (−0.041,0.020) |

Rainfall ^{***} | 0.006 (0.005,0.008) | 0.040 (−0.041,0.113) |

NDVI^{*} | 4.837 (3.589,6.086) | 4.170 (1.308,6.725) |

LSTD** | −0.139 (−0.182,-0.096) | −0.246 (−0.3752,-0.153) |

LSTN^{*} | −0.010 (−0.065,0.085) | 0.124 (−0.031,0.234) |

Year2 | −0.276 (−0.538,-0.013) | 0.242 (−0.356,0.852) |

Year3 | −0.404 (−0.673,-0.135) | 0.441 (−0.244,1.122) |

Cosine | 0.642 (0.477,0.807) | 1.75 (0.570,2.913) |

Sine | 0.533 (0.364,0.701) | 0.522 (−0.597,1.590) |

Amplitude | - | 1.922 (0.941,3.016) |

Shift/phase | - | 0.280 (−0.291,1.033) |

Over dispersion value | - | 0.705 (0.502,1.135) |

Spatial Variation | - | 0.874 (0.516,1.417) |

Temporal variation | - | 0.322 (0.140,0.898) |

Range(3/(^{a} | - | 3.039 (1.337,6.482) |

Zero-Inflated proportion | - | 0.074 (0.004,0.200) |

a: minimum distance in kilometers at which spatial correlation is significant at 5 %,*: environmental average value of the current month of mosquito collection, **: environmental average value of the current and previous month of mosquito collection, ***: environmental total value of the current and two previous month of mosquito collection.

Distance to water bodies, mean value of NDVI during the month of collection and average day temperature during the current and the previous month of collection were associated with mosquito density. In particular, distance to water bodies and average day temperature (LSTD) during the current and the previous month of mosquito collection were negatively related with mosquito density. Mean value of NDVI during the month of collection was positively associated with mosquito density. The average of the total rainfall during the current and the two previous months of mosquito collection, mean night temperature (LSTN) during the month of collection and elevation were not associated with mosquito density. The minimum distance at which the spatial correlation was significant at 5 % was 3.0 km (95 % credible interval: 1.337, 6.482).

The 95 % credible interval of the amplitude parameter revealed a strong monthly variation in mosquito density. The phase of 0.28 radials indicated that the maximum density occured in the months of May and the minimum in November. However, the average mosquito density during the second and third year was not strongly different than that of the first year.

The overall point estimates of annual EIR were 6.7, 9.3 and 9.6 ibpy for the years 2002, 2003 and 2004 respectively. The estimates of EIR for this study were obtained exclusively from the

Distribution of EIR by area in relation to wet and dry months during study period

Area | 2002 | 2003 | 2004 | |||
---|---|---|---|---|---|---|

Wet | dry | Wet | Dry | Wet | dry | |

Asembo | 4.9 | 1.8 | 4.3 | 2.8 | 4.9 | 1.2 |

Gem | - | - | 6.6 | 4.9 | 8.5 | 4.6 |

Figure

Temporal pattern of observed and predicted entomological inoculation rate in relation to rainfall during the study period.

Smooth maps of monthly predicted malaria transmission are shown in Figures

Predicted EIR maps for 2002.

Predicted EIR maps for 2003.

Predicted EIR maps for 2004.

In this study, we described and estimated malaria transmission patterns in the KEMRI/CDC HDSS site using mosquito density and entomological inoculation rate as measures of malaria transmission intensity. Malaria transmission fluctuated over the months (see Figure

The negative association between distance to water bodies and mosquito density in our results implies that many mosquitoes tend to be found close to the water bodies that act as the breeding sites. This probably applies to both newly emerged mosquitoes and adult mosquitoes that have limited dispersal ability. A study of the geographic distribution of adult mosquitoes in the same area also found a significant relationship with water bodies identified in a GIS database during the dry season [

Temperature is an important factor related to mosquito development and survival and to the duration of the sporogonic cycle of the parasite [^{o} C are suitable for stable malaria transmission [^{o} C. In our study, the average day temperature during the current and the previous month of mosquito collection had a strong negative effect on mosquito density.

NDVI, a proxy measure of vegetation was positively associated with mosquito density. The higher the NDVI value the greener the vegetation which is suitable for mosquito development.

The spatial correlation in mosquito density was strong at distances up to about 4 km (95 % credible interval: 2.044, 11.370). However, a study by Midega and colleagues found a maximum distance of mosquito dispersal of only 0.7 km using a capture-recapture technique at the Kenyan coastal region [

The smooth maps generated in this study show that malaria transmission intensity in the HDSS varies over space and time, with high transmission occurring in a few pockets (hot spots). EIR peaks shortly after the onset of the long rains in May of each year. Comparison between the study regions shows that EIR is consistently higher in Gem than Asembo which may be attributable to the occurrence of more rivers and streams in Gem that contribute to the creation of large numbers of mosquito breeding sites. Similarly, substantial differences in the overall EIR between 2002 and 2003 could be due to earlier interventions in some parts of Asembo [

Most analyses of mosquito sporozoite rate, density and EIR in relation to environmental/climatic factors and/or malaria incidence have been based on the assumption of independence between observations. However, mosquito data are usually collected repeatedly over time at fixed geographical locations thus are spatially correlated due to common exposures. Similarly, mosquito density data are count data which are commonly analysed using the Poisson distribution. However, the Poisson distribution assumes that the mosquito average equals the variance which is not always the case with entomological data which usually has a large number of locations with zero mosquitoes even in areas of high transmission. Our proposed Bayesian geostatistical zero-inflation model for assessing the relationship between mosquito density and environmental/climatic factors takes into account the underlying spatial processes and overdispersion associated with observed “excess zeros”. The model has a large number of parameters. However, simulation-based Bayesian computation allows simultaneous estimation of all parameters including the error of the location-specific predictions, a feature missing in the maximum likelihood based framework.

Our work used variable selection method based on standard models. Geostatistical variable selection has been applied in malaria epidemiology [

The maps of EIR produced in this study provide a high resolution exposure surface which is useful in analyzing the impact of transmission on malaria related and all-cause morbidity and mortality. At the same time, these maps help us understand the variability in malaria epidemiology over small areas.

The authors declare that they have no competing interests.

NA conceptualized the statistical method, analyses and interpretation of data, and drafted the paper. NB, KAL and JEG conceived and designed of the entomological study and revised the draft. MH, FO, KFL, LS, and TS helped in interpretation of data and critically revised the draft for intellectual content. PV conceptualized the statistical modeling, interpreted the data and critically revised the drafts for intellectual content. All authors read and approved the final manuscript.

Mosquito density data are typical overdispersed count data, thus modeled using the negative binomial model: Let _{
it
} be the number of mosquitoes at location

Mosquito data used in our analysis are collected at fixed geographical locations, sharing common exposures such as environmental and climatic factors thus correlated in space. To take into account the spatial correlation, we introduce spatial correlation parameter by adding location-specific random effect

In addition to the above spatial correlation, mosquitoes were collected monthly in different locations during the study period and thus correlated in time too. We model temporal correlation by introducing monthly random effects (

Prior distributions of the above model parameters were adopted to complete the Bayesian model specification above. In particular, we choose non-informative Normal prior distribution for the

The Bayesian model was fitted in OpenBUGS version 3.1.2 (Imperial College and Medical Research Council, London, UK). Bayesian Kriging was carried out in a code written by the authors in Fortan 95 (Digital Equipment Corporation) using standard numerical libraries (Numerical Algorithms Group Ltd).

We are grateful to the KEMRI/CDC HDSS for providing the entomological data and to the MTIMBA principal investigators for conceiving the project. The analysis of the data was supported partly by Swiss National Science Foundation (Project Nr. 325200_118379) and a Swiss-South African Joint Research Program (Project No. JRPIZLSZ3_122926). The KEMRI/CDC HDSS is a member of the INDEPTH network.

The findings and conclusions in this study are those of the authors and do not necessarily represent the official views of the Centers for Disease Control and Prevention. This paper is published with the permission of the Director of the Kenya Medical Research Institute.